Known in the art is a call-giving method regarding elevator systems wherein a passenger indicates his/her destination floor already before going into the elevator car by giving a so-called destination call in the elevator lobby. A destination call is generally given either by the aid of a destination call panel in the elevator lobby or by the aid of a personal call-giving device. A personal call-giving device is e.g. an electronically readable ID card or a terminal suited to giving a call. A terminal device is e.g. a mobile phone or a means of communication comparable to it, by the aid of which a passenger can send a destination call to the elevator system by radio. An ID card is e.g. an identifier based on the RFID technology, the data stored in which identifier can be read e.g. with a reader device in the elevator lobby and can be registered as a destination call on the basis of the data read. In conventional destination call systems each passenger must give a destination call to the floor to which he/she is traveling. Also known in the art are destination call systems wherein a passenger can indicate, in addition to the destination floor, also the number of passengers (a so-called group call) traveling along with him/her (in a group). In this case the elevator system allocates one elevator car to the whole group, if the group is sufficiently small to fit into the same elevator car and if the traffic situation of the elevator system permits the allocation in question. The group call described above is, however, problematic because it allows, among other things, misuse and even malicious damage in call-giving such that a passenger moving alone gives a group call to receive for his/her use a “roomy” elevator car. As a consequence of gratuitous group calls, the transport capacity of the elevator system can decrease significantly, which is problematic particularly during a time of upward peak traffic because the arrival of passengers at their destinations is delayed and elevator lobbies can become congested. Another problem is that all the passengers belonging to a group must go to the same destination floor and also that an inspection of the access rights of passengers belonging to the group is not connected to the giving of a call.